Continuous Improvement is an integral part of agile and lean ways of working. Without continuous improvement there is no way to become agile or stay agile if you already are.
Exactly how to continuously improve might vary from team to team. Scrum teams are usually doing Retrospective meetings at the end of each Sprint. Most Kanban teams have borrowed the Retrospective meeting and are doing that on a regular cadence. I have positive experience from doing joint retrospectives in large scale efforts that where complemented by A3 thinking borrowed from lean (since it was too hard to decide on actions across 20 teams with only the initial input).
In a Retrospective the team reflects on how it can improve and decide on experiments to try out. The experiments are followed up so the team can assess if the improvement has been successfully implemented or if new experiments might be needed. If there are no actions/experiments decided in Retrospectives there is no continuous improvements – just complaining sessions that are usually draining a lot of energy.
In some teams the Product Owners are not regularly participating in Retrospective meetings. I believe this is a mistake. First of all, the Product Owner is part of the team and this might be hard to remember if the Product Owners isn’t actively helping the team improve. Secondly, the most important improvements are often related to the communication between users, Product Owner and the Development team. Thirdly it helps the Product Owner get a deeper understanding of issues the Development team is struggling with and that might need prioritization.